f
ńł
�ł0 x " Q )" [0, 1]
f(x) = f : [0, 1] R
ół1 x " Q )" [0, 1]
/
ńł
�łx x = 0 (" x " Z )" [-2, 10]
/
f(x) = f : [-2, 10] R
ół 1
x " Z )" [-2, 10]
x
f : [-a, a] R a > 0
a a
f f(x) dx = 2 f(x) dx
-a 0
a
f f(x) dx = 0
-a
a
f : [-a, a] R a > 0 (f(x)-
-a
f(-x)) dx =
f : R R T T > 0
a+T T
"a " R f(x)dx = f(x)dx.
a 0
f [-Ą, Ą]
Ą Ą
2 2
f(sin x) dx = f(cos x) dx
0 0
Ą
Ą Ą
2
Ą
xf(sin x) dx = f(sin x) dx = Ą f(sin x) dx
2
0 0 0
Ą
x sin x Ą
dx ( ).
1+cos2 x 2
0
1 1
xm(1 - x)n dx = xn(1 - x)m dx n, m " N
0 0
f : R R
x
f(x) = |2 - t| dt
-1
x
f(x) = ||t - 1| - 2| dt
0
 f (2)
ex
sin t
f (x) f(x) = dt x > 0
t
1
x
x
2t+1
f(x) = dt
t2-2t+2
0
[-1, 1]
Ą Ą 2Ą nĄ
lim (sin + sin + � � � + sin ) =
n n n n
n"
1 2 2n-1
lim (n + + � � � + ) =
2
n2 n2
n"
2 2 Ą
" "
lim ("4n2 + + � � � + ) =
2
3
-12 4n2-22 4n2-n2
n"
n (n+1)(n+2)�...�(n+n)
4
lim = a = eln a a > 0
nn e
n"